Vol.2, No.6, 654-666 (2010) Natural Science
http://dx.doi.org/10.4236/ns.2010.26082
Finite element modelling of the pull-apart formation:
implication for tectonics of Bengo Co pull-apart basin,
southern Tibet
Ganesh Raj Joshi*, Daigoro Hayashi
Simulation Tectonics Laboratory, University of the Ryukyus, Okinawa, Japan; *Corresponding Author:
Received 29 January 2010; revised 12 March 2010; accepted 16 April 2010.
ABSTRACT
The tectonic deformation and state of stress are
significant parameters to understand the active
structure, seismic phenomenon and overall ong-
oing geodynamic condition of any region. In this
paper, we have examined the state of stress and
crustal deformation during the formation of the
Beng Co pull-apart basins produced by an en-
échelon strike-slip fault systems using 2D Finite
Element Modelling (FEM) under plane stress co-
ndition. The numerical modelling technique used
for the experiments is based on FEM which ena-
bles us to analyze the static behavior of a real
and continues structures. We have used three
sets of models to explore how the geometry of
model (fault overlap and pre-existing weak she-
ar zone) and applied boundary conditions (pure
strike-slip, transpressional and transtensional)
influence the development of state of stress and
deformation during the formation of pull-apart
basins. Modelling results presented here are
based on five parameters: 1) distribution, orient-
tation, and magnitude of maximum (σH
max) and
minimum (σH
max) horizontal compressive stress
2) magnitude and orientation of displacement
vectors 3) distribution and concentration of st-
rain 4) distribution of fault type and 5) distrib-
ution and concentration of maximum shear str-
ess (σH
max) contours. The modelling results de-
monstrate that the deformation pattern of the
en-échelon strike-slip pull-apart formation is ma-
inly dependent on the applied boundary condit-
ions and amount of overlap between two master
strike-slip faults. When the amount of overlap of
the two master strike-slip faults increases, the
surface deformation gets wider and longer but
when the overlap between two master strike-slip
faults is zero, block rotation observed significa-
ntly, and only narrow and small surface deform-
ation obtained. These results imply that overlap
between two master strike-slip faults is a signi-
ficant factor in controlling the shape, size and
morphology of the pull-apart basin formation.
Results of numerical modelling further show
that the pattern of the distribution of maximum
shear stress (τmax) contours are prominently
depend on the amount of overlap between two
master strike-slip faults and applied boundary
conditions. In case of more overlap between two
masters strike-slip faults, τmax mainly concent-
rated at two corners of the master faults and
that reduces and finally reaches zero at the cen-
tre of the pull-apart basin, whereas in case of no
overlap, τmax largely concentrated at two corn-
ers and tips of the master strike-slip faults. Th-
ese results imply that the distribution and conc-
entration of the maximum shear stress is mainly
governed by amount of overlap between the ma-
ster strike-slip faults in the en-échelon pull-apa-
rt formation. Numerical results further highlight
that the distribution patterns of the displaceme-
nt vectors are mostly dependent on the amount
of overlap and applied boundary conditions in
the en-échelon pull-apart formation.
Keywords: State of Stress; Deformation Regime;
Pull-Apart Formation; Numerical Modelling;
Southern Tibet
1. INTRODUCTION
Pull-apart basins are the prominent feature of topograp-
hic depression structures formed as result of crustal ext-
ension associated with either right-lateral right-stepping
or left-lateral left stepping en-échelon strike-slip fault
systems [1,2]. They usually show a rhombic to spindle-
shape, and occur at different ranges of size from small
sag ponds of few millimeters up to several kilometers

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
655
655
such as the Dead Sea basins [3,4]. The ratio between the
length and width of the pull-apart basins mainly varies
between 3 and 4 [5], but recorded pull-apart basins from
different part of the world show significance differences
in their geometry and structural characteristics [5-7].
Several mechanisms have been proposed for the forma-
tion of the pull-apart basins (Figure 1) but the common
types of mechanism are 1) local extension between two
en-échelon basement strike-slip fault segments 2) a dis-
tributed simple strike-slip shear mechanism and 3) the
Riedel shear mechanisms. The relative motion of the
crust blocks involve in a pull-apart system can either be
parallel or oblique and divided into pure strike-slip, tran-
stensional or transpressional (Figure 2(1)). The forma-
tion of pull-apart basin geometry exhibits different sha-
pes before, during and after the tectonic deformation as
illustrated in Figure 2(2).
(a)
(b)
(c)
(d)
Figure 1. Simple formation of pull-apart basins in strike-slip
systems. (a) Formation of a pull-apart basin along the releasing
band (b) Formation of a pull-apart basin at the termination of a
strike-slip fault (c) Formation of a pull-apart basin at the re-
leasing band and (d) Formation of a pull-apart basin at the
releasing overstep along a strike-slip fault.
(a)
(
b
)
(c)
(1)
(a)
(
b
)
(c)
(2)
Figure 2. (1) General characteristics of strike-slip
pull-apart systems developing in (a) pure strike-slip
(b) transtensional, and (c) transpressional conditions.
(2) Plan view of the formation of pull-apart basin
geometry (a) before and (b) during and (c) after tec-
tonic deformation.

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
656
Pull-apart basins are the preferred sites of concentra-
ted fracturing [8], elevated heat flow [9] and intense sei-
smicity [10-12]. Moreover, they have significant econ-
omical importance and can confine hydrocarbon [13],
significant mineralization [14] geothermal fields [15].
Thus, it is important to study the pull-apart basin and
their relative role for hydrocarbon aspect. In recent years,
many pull-apart basins have been studied extensively in
the several parts of the world [11-17]. Several continen-
tal pull-apart basins have been also documented in the
Tibetan Plateau [11,12] but there is very few studies
have been done to focus the pull-apart basin so far. Pre-
sent study is the first attempt to model numerically Beng
Co pull-apart basin in the southern Tibet.
Numerical modelling is a powerful tool, which prov-
ides useful insights that are beyond direct observations
e.g. stress state, characteristics structures, sequential ev-
olution of the basin, deformation pattern during evolu-
tion of the basin, possible temperature regime and rhe-
ology during and after the pull-apart formation. Theref-
ore, numerical models have been extensively applied for
studying the pull-apart basins [1,2,7,16,18-20]. Segall
and Pollard [16] used the analytical models based on the
infinitesimal strain theory. They maximized the display-
cement near the middle of the faults with the application
of remote external stress. These models provide signify-
cant clues to the orientations of different faults which
can develop inside the overstep area. Gölke et al. [19]
analyzed the vertical displacement and topographic vari-
ations in the releasing overstep along the master
strike-slip faults by using finite element model. Katzman
et al. [1] applied the 3D boundary element models of
pull-apart basin and compared the modelling results to
the Dead Sea Basin. Their results show that the basin de-
formation mainly depends on the width of the shear zone
and on the amount of the overlap between the basin-
bounding faults. Petrunin and Sobolev [2,20] presented
the 3D thermo-mechanical models of the pull-apart basin
developed at an overstepping of an active continental
transform faults, and found that the thickness of the brit-
tle layer beneath the basin has significant role in control-
ling the dimension and deformation pattern of the basin.
From their modeling, they further conclude that the deep
narrow pull-apart basins are relatively well developed in
cold lithosphere, as in the Dead Sea Basin and require
very low friction at major faults [2]. Although numerical
modelling studies have been applied extensively for sim-
ulating deformation in the pull-apart basins, but much
less is known overall kinematics or geodynamics within
the shallow pull-part structure, as it is filled by uncon-
solidated sediments, high structurally disrupted or cryst-
allizing materials (veins/plutons).
The purpose of this paper is to understand the relat-
ionship between fault geometry; applied boundary cond-
itions (pure strike-slip, transtensional and transpressio-
nal), imposed displacements with state of stress and tect-
onic deformation pattern within a releasing overstep alo-
ng the two en-échelon strike-slip pull-apart formation ap-
plying different sets of models. We have used a series of
2D finite element calculations incorporating elastic rheo-
logy under plane stress condition using Mohr-Coulomb
failure criterion of faults formation.
2. GEOLOGY AND TECTONIC SETTING
The tectonic evolution and uplift of the Tibetan Plateau are
a result of tectonic events which occurred due to Indian
and Asian plate convergence [21]. The continuing north-
ward movement of the Indian plate for the past 10 Myr
has lead to the Tibetan Plateau experiencing widespread
extension as indicated by the large scale normal faults
and strike-slip zones that made several extensional fea-
tures such as graben, rift-systems and pull-apart basins
in Late Quaternary time [12,21,22]. The tectonic evolu-
tion and contemporary states of stress on the Tibetan
plateau are mainly governed by E-W extension and N-S
compression. The present day average state of stress of
the Tibetan Plateau is subject to an extensional (σ3) axis
trending 112 ± 6° and the minimum horizontal stress (σH min)
trajectory trends WNW-ESE. The compressional (σ1)
axis trends 022 ± 6° and the maximum horizontal stress
(σH max) trends N-S to NNE-SSW direction, roughly par-
allel to the Indian-Eurasian convergence in the central
part of the India-Asia collision zone [22].
The Beng Co basin is en-échelon strike-slip pull-apart
basin named after the 25 km long and 7 km wide Beng
Co lake. It developed within the Late Ceneozoic time
[12], and is located at 31°10’N and 91°10’E (Figure 3).
It is about 40 km long with an average strike of north
122°E originating from the long side of Beng Co and
extending toward the NW and SE strike-slip fault zone.
Geological field observations along the Beng Co can
identify, two major fault strands and composed of series
of en-échelon pull-apart basins. An en-échelon arrange-
ment of the mole tracks in the field implies possible ev-
idence of the right-lateral strike-slip nature of the Beng
Co pull-apart [11]. The Beng Co Fault Zones (BCFZ)
cut obliquely across folded Jurassic black shale and calc-
schists, whereas the southern branch of the fault zone
runs mostly in the granites and the Jurassic shales. The
northern exposure of the BCFZ cuts highly folded, early-
to-middle Cretaceous red sandstone which lie unconfo-
rmably upon the Jurassic shales [11]. Further northwest,
it passes through the area where ophiolites have been
thrust southward on the Jurassic shales and truncates

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
657
657
Figure 3. Seismotectonic map of the Beng Co region after (Ar-
mijo, 1989). Fault plane solution of July 22, 1972, earthquake
is from Molnar and Chen (1983) [33]. Black arrows represent
tensional directions deduced from analysis of recent minor
faults are from Mercier et al. (1987) [22].
towards the gently folded conglomerates. The southern
branch of the BCFZ lies along the southern edge of a
NW-SE granite range.
3. SEISMICITY OF THE REGION
The Tibetan Plateau is one of the highest and most active
region of the world, which evolved as a consequence of
the collision between India and Eurasia landmasses
about 50 Ma ago [21]. The continuous northward pene-
tration of Indian crust within Eurasia resulted significant
amount of stress accumulation, causing intense seismic-
ity and active tectonic nature of the plateau. In the Ti-
betan region, seismicity is observed mostly from shallow
to intermediate depths. Generally, the seismic pattern
shows diffuse in nature and does not follow any known
particular tectonic trends. The focal mechanisms solu-
tions here are predominantly of normal and strike-slip
type, which further attributed to the large scale E-W ex-
tension of the region [23].
The field observations provide several evidences of
Quaternary displacements, ruptures and large offsets on
either side of the Beng Co pull-apart basin. Several pro-
minent, continuous and fresh surface breaks with large
numbers of paleoseismic events along the zone imply
that the Beng Co pull-apart region is seismo-tectonically
active in contemporary time. Evidence includes several
major earthquakes including November 17 and 18, 1951
(MW = 8); August 17, 1952; December 28, 1951 and July
12, 1972, which show a magnitude (MW) > 6, and are
located near the southern extremity of the Beng Co
pull-apart (Figure 3).
4. MODELLING
Numerical simulations are essential for creating an un-
derstanding of the physics behind the observations of
surface displacement and strain. This is particularly im-
portant for understanding data related to active tectonics
and earthquake phenomenon because earthquake cycles
occur on timescales of thousands of years and our ob-
servations sample only a small part of that system. The
numerical modelling technique used for the experiments
is based on a Finite Element Modelling (FEM) which
enables us to analyze the static and behavior of real and
continuous structures. FEM has successfully proved to
be a powerful method for simulating pull-apart basin
geometries and deformation mechanisms, [1,2,7,16,18,
19]. In this study, we applied a 2D-finite element softw-
are package developed by Hayashi [24], which has been
used widely by Joshi and Hayashi, [25-27]. Similar to
most mesh-based numerical methods, bodies of rocks in
this program are represented by triangular elements and
each element is assigned appropriate material properties,
such as density, Young’s modulus, cohesion and angle
of internal friction. The mesh deforms and moves with
respect to material and able to compute appropriate def-
ormation in the program. The details of mathematical
formulations about the software package have already
described by Hayashi [24].
4.1. Model Setup
The dimension of the models are 42 km in length and 7.5
km in width which mimic the natural dimension of the
Beng Co pull apart basin adopted after Armijo et al. [11]
(Figure 3). We simplified the model and divide the mo-
del area into triangular mesh and several domains. The
initial mesh of the model consists of 546 nodal points,
984 triangular elements and two master right-lateral
strike-slip faults. In the model, we assumed that the up-
per crust is a brittle layer and is treated as elastic mate-
rial. In order to simulate the brittle deformation mecha-
nism of the model, we adopt elastic rheology under
plane stress conditions. In our model, the crust up to 20
km is considered to behave as an elastic material be-
cause of its brittle nature and presence of earthquake and
faults. Rocks forming the brittle crust of the earth con-
tain inhomogeneities which may result in differences
compared with our homogeneous and uniform model. In
spite of these limitations, our models are still able to
yield valuable information related to the pull-apart for-
mation.
4.2. Boundary Condition
For the modelling purpose, a two dimension Cartesian
rectangular simplified model which shows original ge-

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
658
ometry of the Beng Co pull-apart basin has been adopted
after Armijo et al. [11] (Figure 4). Far-field plate veloc-
ity boundary conditions are enforced at the either side of
the Beng Co Fault Zones (BCFZ). The brittle crust is
divided into three simple domains, which may exhibit
dissimilar rock layer properties. Domain 1 and 2 repre-
sent the southern and northern flank of the pre-existing
BCFZ, and domain 3 represents surrounding regions.
We consider typical two types of models 1) a model with
a pre-existing pull-apart basin and 2) a model without
pre-existing pull-apart basin. The model without a
pre-existing pull-apart basin is further tested into differ-
ent overlap/separation ratios (Model B and Model C).
We imposed three types of reasonable boundary condi-
tions to mimic the possible natural strike-slip environm-
ent of the pull-apart formation. These displacement bou-
ndary conditions are 1) pure strike-slip 2) transtensi-
onal and 3) transpressional conditions (Figure 4). The
empirical 100 to 500 m displacements were imposed
from northern-left and southern-right corners in different
boundary environments, and only 10% of imposed dis-
placement is considered for transtensional and transpres-
sional conditions for modelling (Figure 4).
4.2.1. BC1: Pure Strike-Slip Model
The pure en-échelon strike-slip boundary conditions
were obtained by moving the upper left-hand and lower-
right hand corners using displacement in the left (–X)
and right (+X) directions while the lower and upper
edges are fixed (Figure 4(a)). This boundary condition
explores the effect of pure-strike-slip movements on the
overall stress field and faulting regime on the pull-apart
formation.
4.2.2. BC2: Transtensional Model
The transtensional boundary conditions were simulated
by moving the upper left-hand and lower-right hand
corners using displacement in the left (–X) and right (+X)
directions, and adding an outward displacement in left
(–Y) and right (+Y) directions to the lower and upper
edges of the model respectively (Figure 4(b)). This bou-
ndary condition provides the opportunity to understand
the distribution and orientation of the stress field and
deformation style of the transtensional environment of
the pull-apart formation.
4.2.3. BC3: Transpressional Model
In order to investigate the state of stress and overall defor-
mation of the strike-slip pull-apart basin we applied tran-
spressional boundary condition. The transpressional boun-
dary condition were obtained by moving the upper left-
hand and lower-right hand corners using displacement in
the left (–X) and right (+X) directions with adding an in-
ward displacements in left (–Y) and right (+Y) directions
to the lower and upper edges, respectively (Figure 4(c)).
4.3. Mechanical Parameters and Rock
Domain Property
The mechanical properties such as density (ρ), Young’s
modulus (E), Poisson’s ratio (υ), angle of internal fric-
tion () and cohesive strength (c) are important rock
Model A Model BModel C
(a) Pure Stnike-Slip condition
(b) Trantensional condition
(c) Transpressional condition
Domain 1
Domain 2Domain 1
Domain 2
Domain 3
Domain 1
Domain 2
Domain 1
Domain 2
Domain 1
Domain 2
Domain 3
Domain 1
Domain 2
Domain 3
Domain 1
Domain 2
Domain 3
Domain 1
Domain 2
Domain 3
Domain 1
Domain 2
Domain 3
Figure 4. Simplified finite element model partition with geometry and boundary conditions for Models
A, B and C. The triangular elements show the finite element grid.

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
659
659
parameters in the FEM analysis (Table 1). The density
(ρ) was obtained from the interval velocity of the indi-
vidual rock domain, using the relation proposed by Bar-
ton [28] and compared them with published velocity
model [29] from southern Tibet. Seismic P-wave (Vp)
and S-wave (Vs) velocities are chosen from the published
literature of the study area [30]. We have used two in-
dependent elastic constants, Young’s modulus and Pois-
son’s ratio to solve the following elastic equations in the
brittle part of the lithosphere [24,31].
)1(
)21)(1(
2
v
vv
VE p


 
(1)
2
11
[1 ]
2()1 ps
vVV 

(2)
where E-Young’s modulus, υ -Poisson’s ratio, ρ -density
of rock, Vp- seismic P-wave velocity and Vs- seismic
S-wave velocity.
In performing FEM calculation, the whole model is
divided into 3 domains and each domain has been allo-
cated distinct rock layer properties on the basis of pre-
dominant rock types (Table 1). In case of Model A, we
assume that BCFZ is pre-existing weak shear zones
which allowed us to adopt the value of Young’s modulus
less compared to other rock domain.  and c were ob-
tained from the Handbook of Physical Constants [32].
5. MODELLING RESULTS
To understand the various factors that control the induced
state of stress and deformation pattern of the pull-apart
basin formation, we have carried out a number of mod-
elling experiments for two characteristic models 1) with
a pre-existing pull-apart basin in model and 2) without a
pre-existing pull-apart basin in model.
In case of without pre-existing pull-apart basin, we fur-
ther calculated by two separate models, i.e., Model B and
Model C. The Model B which represents no overlap or
zero overlap between the two master faults and the Mo-
del C corresponds to considerable overlap between two
master en-échelon basement strike-slip faults. Each of
these models was run for the three most common types
of boundary conditions of pull-apart formation: 1) BC1:
pure strike-slip condition, 2) BC2: transtensional condi-
tion, and 3) BC3: transpressional condition. Here, mod-
elling results are represented based on 1) the maximum
(σH
max) and minimum (σH min) horizontal principle stress
2) magnitude and orientation of the displacement vectors
3) distribution and magnitude of the strain 4) distribution
of fault type and 5) concentration and distribution of the
maximum shear stress (τmax) contours. The direction and
magnitude of the maximum compressive stress axis and
minimum compressive stress axis are represented by σ1
and σ3, respectively. In addition, we have calculated
tectonic deformation and faulting regime on the Beng Co
pull-apart basin based on the relation and position of the
σ1, σ2 and σ3 applying Mohr-Coulomb failure criterion.
5.1. Model A: Pre-Existing Pull-Apart Basin
Figures 5, 6 and 7 illustrate the orientation of the max-
imum (σH
max) and minimum (σH min), horizontal prin-
ciple stress trajectories, strain distribution, displacement
vectors, contour lines of maximum shear stress (τmax)
and development of a faulting regime for Model A in the
pure strike-slip boundary condition. The calculated σH
max trajectories show almost N-S directional orientation
with uniform distribution in the model with minor varia-
tion in the upper left and lower right corners, which cor-
responds to the direction of maximum shortening of the
Tibetan Plateau (Figures 5(a), 6(a) and 7(a)). Similarly,
σH min trajectories show more or less E-W orientation,
which is also consistent with the direction of maximum
extension in the Tibetan Plateau (Figures 5(b), 6(b) and
7(b)). However, some discrepancy was observed in the
corners of the models which might be due to boundary
effect. The orientations of the displacement vectors show
prominent difference among three boundary conditions.
The major discrepancy was obtained at the upper-right
corner and lower-left corners of the pull-apart basin
(Figures 5(c), 6(c), 7(c)). Figures 5(d), 6(d) and 7(d)
illustrate the predicted strain partitioning for Model A,
where high extensional strain is mainly concentrated
along pre-existing weak shear zone. This is due to weak
rheology, and consistent with the applied model geome-
try. The predicted faulting pattern shows almost similar
predominantly strike-slip type of faults for all boundary
conditions (Figures 5(e), 6(e) and 7(e)). Figures 5(f),
6(f) and 7(f) show concentration and distribution pat-
terns of modeled τmax contours for all three boundary
conditions, where τmax is largely confined at the central
part of the pull-apart basin.
5.2. Without Pre-Existing Pull-Apart Basin
In this case, two models (Model B and Model C) were
used to calculate state of stress and deformation regime
Table 1. Rock mechanical properties used for different do-
mains in the finite element models.
Rock Domain ρ (kg/m3) E (GPa) c (MPa)
 (deg.)
Domain 1 2900 60.0 24.0 50.0
Domain 2 2000 01.0 10.0 31.0
Domain 3 2000 01.0 10.0 31.0

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
660
Model A: BC 1
a) σ
H max
b) σ
H min
c) displacement
vectors
d) strain
e) fault type
f) τ
max
100 Mpa -
100 Mpa - 100 Mpa -
100 Mpa -100 Mpa -
100 Mpa -
t
t
1e3 1e2 1e2
0.05
0.05 0.05
12
10
8
6
4
2
12
10
8
6
4
2
12
10
8
6
4
2
10 20 30 40 10 20 30 4010 20 30 40
Figure 5. Results of Model A for all three pure strike-slip, transtensional and transpressional boundary conditions. (a) Maximum
compressional stress (1) trajectories (b) Maximum extensional stress (3) trajectories (c) strain distribution (d) displacement vectors
(e) faulting regime and (f) distribution of maximum shear stress (max) contours under 100 m boundary displacement condition at 10
km depth.
of the Beng Co pull-apart basin for understanding the
effect of different overlap on the stress distribution.
Figures 6 and 7 illustrate the calculated maximum (σH
max) and minimum (σH min) horizontal principle stress
trajectories, strain distribution, displacement vectors,
contour lines of maximum shear stress (τmax) and devel-
opment of faulting regime of the Model B and Model C.
In both models, orientations of the σH min trajectories
show more or less E-W directed orientation for all
boundary conditions, which is consistent with E-W ex-
tension environment of the Tibetan Plateau. A compari-
son of the Model B and Model C shows that although
the general stress (σH
min) patterns remain similar, there
are significance differences in the distribution and con-
centration of τmax (Figures 6(f) and 7(f)). Similarly, ac-
cording to applied boundary conditions, the orientation
and magnitude of displacement vectors show significant
variations between Model B and Model C (Figures 6(c)
and 7(c)). There are no considerable differences ob-
served in the predicted strain partitioning among both
models, where strain is mainly concentrated along the
fault zone which is due to weak rheology. The predicted
faulting pattern of the model exhibits almost similar
predominantly strike-slip types of faults that have de-
veloped for all boundary conditions. If we compare
pre-existing pull- apart model (Model A) there is sig-
nificant difference in distribution and concentration of
τmax contours.
5.2.1. Model B: Without Overlap on the
Pull-Apart basin
Model B illustrates the results of numerical simulation in
the case of no pre-existing pull-apart basin and zero
overlap of the two master strike slip faults in the model.
Figure 6 illustrates the orientation of σH max and σH min
trajectories, displacement vectors, strain concentration,
distribution of τmax contours and faulting regimes for
Model B. In this model orientation of σH max trajectories,
strain concentration and faulting regimes which show
similar results for all boundary conditions at the same
displacement, compared to Models A and C. However,
the magnitude of the σH min trajectories shows little dif-
ferences between BC1 and BC3, and the predicted re-
sults of displacement vectors and distribution of τmax show
considerable differences between three applied boundary

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
661
661
conditions. Figure 6(c) illustrates the principal variations
of predicted displacement vectors among three boundary
conditions (i.e., BC1, BC2 and BC3) for Model B. Simi-
larly, Figure 6(f) shows how differently τmax is distrib-
uted for the different boundary conditions in Model B.
5.2.2. Model C: With Fault Overlap on the
Pull-Apart Basin
Model C predicted the results of numerical simulation
taking into account pre-existing overlap of the two mas-
ter strike slip faults in the Beng Co pull-apart basin.
Figure 7 illustrates the orientation of σH
max and σH min
trajectories, displacement vectors, strain concentration,
distribution and accumulation of τmax and overall faulting
regimes for Model C. Results show that there are no
considerable variations of the distribution and orienta-
tion of the predicted σH
max and σH min trajectories, strain
partitioning and faulting regime. Nevertheless, high disc-
repancies do exist in case of displacement vectors (Fig-
ure 7(c)) and distribution and concentration of τmax con-
tours (Figure 7(f)). If we compare distribution and con-
centration of τmax to other models the Model C does not
predict τmax in the centre of the pull-apart basin which is
possibly due to the fault overlap geometry. Moreover,
major difference appear in predicted the maximum ext-
ensional stress (σ3) trajectories within the Model C
(Figure 7(b)), which might be the cause of the applied
boundary condition.
6. DISCUSSIONS
6.1. Effect of Pre-Existing Weak Shear Zone
of Pull-Apart Basin
We first explore the effect of a pre-existing weak shear
zone of pull-apart basin on the stress field and deforma-
tion pattern during formation of the pull-apart basin.
Figure 5 illustrates the modelling results of a pre-exist-
ing weak shear zone of Beng Co strike-slip pull-apart
basin. In order to quantify the relative importance of a
pre-existing strike-slip weak shear zone on the pull-
apart basin the modelling results are compared between
Model A and Model B. A close examination of results of
Model B: BC 1
a) σ
H max
b) σ
H min
c) displacement
vectors
d) strain
e) fault type
f) τ
max
100 Mpa -
100 Mpa -
100 Mpa -100 Mpa -
100 Mpa -
C2
1e3 1e3
0.05 0.05 0.05
12
10
8
6
4
2
10 20 30 40 10 2030 4010 20 30 40
100 Mpa -
ent
C3
ent 1e3
12
10
8
6
4
2
12
10
8
6
4
2
Figure 6. Results of Model B for all three pure strike-slip, transtensional and transpressional boundary conditions.(a) Maximum
compressional stress (1) trajectories (b) Maximum extensional stress (3) trajectories (c) strain distribution (d) displacement vectors
(e) faulting regime and (f) distribution of maximum shear stress (max) contours under 100 m boundary displacement condition at 10
km depth.

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
662
Model C: BC 1
a) σ H max
b) σ H min
c) displacement
vectors
d) strain
e) fault type
f) τ max
100 M
p
a - 100 M
p
a -100 M
p
a -
2
1e3 1e3
0.05 0.05 0.05
12
10
8
6
4
2
10 20 30 40 10 2030 4010 20 30 40
ent ent 1e3
100 M
p
a - 100 M
p
a -100 M
p
a -
12
10
8
6
4
2
12
10
8
6
4
2
a) σ
H max
b) σ
H min
f)τ
max
Figure 7. Results of Model C for all three pure strike-slip, transtensional and transpressional boundary conditions. (a) Maximum
compressional stress (1) trajectories (b) Maximum extensional stress (3) trajectories (c) strain distribution (d) displacement vectors
(e) faulting regime and (f) distribution of maximum shear stress (max) contours under 100 m boundary displacement condition at 10
km depth.
these two models demonstrate that major disparities ex-
ist in the horizontal displacement vectors and distribu-
tion and concentration of τmax contour lines, whereas
minor differences also exist with regards to the orienta-
tion and magnitude of the horizontal principal stresses
and deformation pattern, which indicate that the effect of
the pre-existing weak shear zone of the pull-apart basin
are important control on distribution and concentration
of τmax, and principal stresses direction.
6.2. Effect of Change in Boundary
Conditions in Pull-Apart
Formation
Boundary conditions are important factors for control-
ing the stress state and deformation patterns of the model.
Therefore, we explore the effect of a change in boundary
conditions on the stress field and deformation style in
the formation of the pull-apart basin. In order to investi-
gate the effect of boundary conditions in stress field and
deformation patterns, we have tested three types 1) pure
strike-slip 2) transtensional and 3) transpressional of
boundary conditions. Figures 5, 6 and 7 show predicted
modelling results of the σH max, σH min, τmax, displacement
vector, strain partitioned and faulting regime for all three
models. Modelling results clearly demonstrated that the
distribution and concentration of τmax, displacement
vectors and dimension of the pull-apart basin in each
boundary condition varies significantly, while orienta-
tions of the σH max and σH min are moderately influenced
and faulting regime is not effected by changing applied
boundary conditions.
6.3. Effect of Change in Fault Overlap in
Pull-Apart Development
To investigate the effect of change in the two en-échelon
faults overlap geometry we have considered two sepa-
rate models having 1) zero fault overlap (Model B), and
2) with fault overlap (Model C). Figure 7 shows the
predicted result of fault overlap Model C. If we compare
the predicted results of this model with other two models
(Model A and Model C) (Figures 6 and 7) we observed
that the major differences among models are in the ori-
entation of displacement vectors, and distribution and
concentration of the τmax contours. The large rotation of

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
663
663
the horizontal displacement vector appears in the central
part of the pull-apart basin with zero overlap model
(Model B), while no significant rotation of displacement
vector observed in the overlap model (Model C). The
Model C produced a tentative rectangular and wide pull-
apart basin, while Model B produced a narrow and small
pull-apart basin (Figures 6 and 7). Moreover, simulated
results from our models clearly show that if the faults
overlap increases, the size of the pull-apart basin also
increases and if the fault overlap decreases the size of
the pull apart basin decreases, considerably. These resu-
lts of numerical modelling imply that fault overlap ge-
ometry has an extensive control on the change in shape,
size and morphology of the pull-apart formation, which
is consistent with previous studies such as Gölke, et al.,
[19]. Moreover, fault overlap geometry has significant
effect on distribution and orientation of σH
min and con-
centration of the τmax contours but there is no effect on
the development of fault type (Figures 6 and 7).
6.4. Effect of Change in Displacement in
Pull-Apart Formation
The applied displacement is another significant factor
that strongly influences on the magnitude and orientation
of the stress field and deformation pattern. We have in-
vestigated the effect of applied displacement on the de-
formation and stress regime during the pull-apart deve-
lopment. We have used 100 to 500 m displacement con-
ditions from the either sides of the model. Our modelling
results clearly show that displacement has a major effect
on the magnitude and orientation of the maximum (σH
max)
and minimum (σH
min) horizontal stresses and displace-
ment vectors, but minor effect on the style of faulting.
This result indicates that the change in displacement
significantly influences the magnitude of the stress traj-
ectory but only has a limited effect on the orientation of
the pull-apart formation. We have further explored the
influence of change in displacement on maximum shear
stress (τmax) concentration. The model results demon-
strate that if we increase the applied displacement the
magnitude and concentration of the τmax contour in-
creases considerably and shear strain will become con-
centrated in the two ends of the master fault zones.
7. CONCLUSIONS
A two-dimension finite element numerical model was
used to simulate the strike-slip pull-apart basin forma-
tion. We examine the state of stress and deformation ass-
ociated with the right-lateral, en-échelon Beng Co pull-
apart basin in the southern part of Tibetan Plateau. In
this paper, we have considered three models each incor-
porating three different boundary conditions (pure strike-
slip, transtensional and transpressional) with different
amount of fault overlap of the master strike-slip fault sy-
stems. Our modelling results demonstrate that the defor-
mation pattern of the en-échelon strike-slip pull-apart fo-
rmation is mainly dependent on the geometry of the pull-
apart basin, applied boundary conditions and the amount
of overlap between two master strike-slip fault systems.
When the amount of overlap of the shear zone increases,
the surface deformation gets wider and longer between
two master faults, but if zero overlap exists between the
two strike-slip fault systems, the narrow pull apart for-
med and block rotation is observed within the pull-apart
basin. Based on present modelling we conclude that ove-
rlap between two en-échelon strike-slip faults is a signi-
ficant factor in controlling the shape, size and morphol-
ogy of the pull-apart formation.
The pattern of the rotation of displacement vectors and
maximum shear stress (τmax) distribution contours are
also highly dependent on the applied boundary condi-
tions and amount of overlap. In the case of a larger
overlap, τmax is mainly concentrated at two corners of the
master strike-slip faults and reduces toward the centre of
the pull-apart basin, whereas for zero overlap conditions,
τmax is largely concentrated at the two corners and tips of
the master strike-slip faults. These results imply that the
concentration and distribution of the maximum shear
stress (τmax) is principally governed by amount of over-
lap between the master strike-slip faults in the
en-échelon pull-apart formation.
Finally, on the basis of our modelling results we can
conclude that the adopted geometry, applied boundary
conditions and amount of overlap of the shear zone have
a remarkable role in controlling the overall dimension,
stress distribution and deformation pattern during the
pull-apart formation.
8. ACKNOWLEDGEMENTS
G. R. Joshi gratefully acknowledges the Ministry of Education, Sports
and Culture (Monbukagakusho) Japan for the financial support to
accomplish this research. The authors wish to thank simulation tecton-
ics laboratory members for their help and support during the research.
REFERENCES
[1] Katzman, R., Brink, U.S. and Lin, J. (1995) Three di-
mension of modelling of pull-apart basins: Implications
for the tectonics of the Death Sea Basins. Journal Geo-
physical Research, 100(B4), 6295-6312.
[2] Petrunin, A. and Sobolev, S.V. (2006) What controls the
thickness and lithospheric deformation at a pull-apart ba-
sin? Geology, 34(5), 389-392.
[3] Burchfiel, B.C. and Stewary, J.H. (1966) Pull-apart ori-
gin of the central segment of the Death valley. Geologi-
cal Society of America, 77(4), 439-442.

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
664
[4] Sylvester, A.G. (1988) Strike-slip faults. Bulletin of Geo-
logical Society of America, 100(11), 1666-1703.
[5] Ayden, A.A. and Nur, A. (1982) Evolation of pull-apart
basins and their scale independence. Tectonics, 1(1), 91-
105.
[6] Gamond, J.F. (1983) Displacement feature associated
with fault zone: A comparison between observed exam-
ples and experimental models. Journal of Structural Ge-
ology, 5(1), 33-45.
[7] Bahat, D. (1983) New aspects of rhomb structures.
Journal of Structural Geology, 5(6), 591-601.
[8] Connolly, P. and Cosgrove, J. (1999) Prediction of frac-
ture-induced permeability and fluid flow in the crust us-
ing experimental stress data. AAPG Bulletin, 83(5), 757-
777.
[9] Hu, S., O’Sullivian, B.P., Raza, A. and Cona, B.P. (2001)
Thermal History and tectonic subsidence of the Bohai
Basin, northern China: A Cenozoic rifting and pull-apart
basins. Physics of the Earth and Planetary Interiors,
126(3-4), 121-135.
[10] Armijo, R., Meyer, B., Navarro, A., King, G. and Barkar,
A. (2002) Asymmetric slip partitioning in the Sea of
Marmara pull-apart: A clue to propagation processes of
the North Anatolian Fault. Terra Nova, 14(2), 80-86.
[11] Armijo, R., Tapponnier, P. and Tonglin, H. (1989) Late
Cenozoic right-lateral strike-slip faulting in southern Ti-
bet. Journal of Geophysical Research, 94(B3), 2787-
2938.
[12] Armijo, R., Tapponnier, P., Mercier, L. and Tonglin, H.
(1986) Quaternary extension in southern Tibet: Field ob-
servations and tectonic implications. Journal of Geo-
physical Research, 91(B14), 13803-13872.
[13] Harding, T.P. (1990) Identification of wrench faults using
sub-surface structural data: Criteria and pitfalls. AAPG
Bulletin, 74(10), 1590-1609.
[14] Recherds, P.D., Boyce, A.J. and Pringle M.S. (2001)
Geological evolution of the Escondida area, northern
Chile: a model for spatial and temporal localization of
porphyry Cu mineralization. Economic Geology, 96(2),
271-305.
[15] Monastero, F.C., Katzenstein, A.M., Miller, J.S., Unruh, J.
R., Adams, M.C. and Richerds-Dinger, K. (2005) The
Coso geothermal field: A nascent metamorphic core
complex. Bulletin of Geological Society of America,
117(11-12), 1534- 1553.
[16] Segall, P. and Pollard, D.O. (1980) Mechanics of discon-
tinuous faults. Journal of Geophysical Research, 85(B8),
4337-4350.
[17] Basile, C. and Brun, J.P. (1999) Transtensional faulting
pattern from pull-apart basin to continental margins: An
experimental investigation. Journal of Structural Geol-
ogy, 21(1), 23-37.
[18] Du, Y. and Aydin, A. (1993) The maximum distortion
energy density criterion for shear fracture propagation
with applications to the growth paths of en-échelon faults.
Geophysical research Letters, 20(11), 1091-1094.
[19] Gölke, M., Cloetingh, S. and Fuch, K. (1994) Finite ele-
ment modelling of pull-apart formation. Tectanophysics,
240(1-4), 45-57.
[20] Petrunin, A. and Sobolev, S.V. (2008) Three-dimensional
numerical models of the evolution of pull-apart basins.
Physics of Earth and Planatery Interiors. 171(1-4), 387-
399.
[21] Molnar, P. and Tapponier, P. (1975) Cenozoic tectonics of
Asia: Effects of a continental collision. Science , 189(4201),
419-426.
[22] Mercier, J.L., Armijo, R., Tapponinier, P., Carey-Gail-
hardis, E. and Han, T.L. (1987) Change from late tertiary
compression to late quaternary extension, in southern
Tibet, during the India-Asia collision. Tectonics, 6(3),
275-304.
[23] Torre, T.L. de la, Monsalve, G., Sheehan, A.F., Sapkota, S.
and Wu, F. (2007) Earthquake processes of the Himala-
yan collision zone in eastern Nepal and the southern Ti-
betan Plateau. Geophysical Journal International, 171(2),
718-738.
[24] Hayashi, D. (2008) Theoretical basis of FE simulation
software package. Bulletin of the Faculty of Science,
University of the Ryukyus, 85, 81-95.
[25] Joshi, G.R. and Hayashi, D. (2008a) Neotectonic defor-
mation and shortening along the Himalayan front in the
Garhwal region by finite element modelling. Bullettino di
Geofisica Teorica ed Applicacate, 49, 228-233.
[26] Joshi, G.R. and Hayashi, D. (2008b) Numerical model-
ling of neotectonic movements and state of stresses in the
central seismic gap region, Garhwal Himalaya. Journal
of Mountain Science, 5(4), 279-298.
[27] Joshi, G.R. and Hayashi, D. (2010) Development exten-
sional stresses in the compressional setting of the Hima-
layan thrust wedge: Inference from numerical modelling.
Natural Science (in press).
[28] Barton, P.J. (1986) The relationship between the seismic
velocity and density in the continental crust—a useful
constraint? Geophysics Journal of the Royal Astronomi-
cal Society, 87(1), 195-208.
[29] Zhao, W., Nelson, K.D. and Project INDEPTH Team
(1993) Deep seismic reflections evidence for continental
underthrusting beneath south Tibet. Nature, 366(6455), 557-
559.
[30] Cogan, M.J., Nelson, K.D., Kidd, W.S.F., Wu, C. and
Project INDEPTH Team (1998). Shallow structure of the
Yadong-Gulu rift, southern Tibet, from refraction analy-
sis of Project INDEPTH common midpoint data. Tecton-
ics, 17(1), 46-61.
[31] Timosenko, S.P. and Goodier, J.N. (1970) Theory of
elasticity. 3rd Edition, McGraw-Hill Book Company,
London.
[32] Clark, Jr., S.P. (Ed.) (1966) Handbook of Physical Con-
stants. New York, Geological Society America, Memoir.
[33] Molnar, P. and Chen, W.P. (1983) Focal depths and fault
plane solutions of earthquakes under the Tibetan Plateau.
Journal of Geophysical Research, 88(B2), 1180-1196.

G. R. Joshi et al. / Natural Science 2 (2010) 654-666
665
665
Appendix
Appendix A is quoted from “Theoretical basis of FE
simulation software package” page 84 to 89 written by
Hayashi (2008).
1. 2D Elastic Problem
The principle of virtual work is described that the exter-
nal works done by virtual displacement equals the inter-
nal work done by virtual strain. Let us consider a certain
element within a domain concerned as shown in Figure
A1. When small displacement i u, which is called vir-
tual displacement, is applied to deform the element
without disturb the balance of system, the external work
is written as

e
T
e
Wfu where 










3
2
1
u
u
u
ue and 










3
2
1
f
f
f
fe
While taking e as virtual strain derived from virtual
displacement and s as stress, the strain energy of the
element are shown as
 dSU
S
Tse


According to the principle of virtual work, both must
be equated. W = U
  dS
S
T
e
T
esefe 
 (1)
ca













a
a
a
x x
xaxaa
xaau
0
ii
2
1
0
21
2211
0
)1(
Figure A1. Force vector and virtual displacement vector work
at each nodal point in a certain finite element (Hayashi, 2008).
Then, to obtain the practical form of (1), we assume
the displacement within element as a function of coor-
dinates. Since the simplest relation is linear, we take
linear relation as follows.

 dS
T
s
ee
T
esefu 

Substituting the values of coordinate and displacement
at nodes into this equation, we have
a)1( N2N1N
x
x
u

Writing in vector form
aau C
x x
x x
x x
u
u
u























3231
2221
1211
3
2
1
e
1
1
1
The coefficient vector a is derived from the equation,
e
Cua 1

















332313
322212
312111
11
C
and C det


and C of cofactor
ij


.
Therefore, the inner displacement is represented in
terms of nodal displacements
e
e
xx
xx xx
C u
u)
(
1
uc
23213231
2231222121311211
1






Replacing as )(
1
23121 xx NNNN 

 
, we have
NN uu


.
Since we will consider 2D situation, displacement has
2 components as u1 and u2.
11 NN uu


22 NN uu


Writing them in vector form,




















2
1
321
321
2
1
000
000
u
u
u
u
u


Then, exchanging the order of nodal displacements,
323122211211322212312111 uuuuuuuuuuuu 
e
u
u
u
u
u
u
u
u
u
u


































32
31
22
21
12
11
321
321
2
1
000
000



G. R. Joshi et al. / Natural Science 2 (2010) 654-666
666
Then, we can represent strain by nodal displacements
as
e
e
B
uu
u
u
e
e
e
u
ue



































1,32,31,22,21,12,1
2,32,22,1
1,31,21,1
1,22,1
2,2
1,1
12
22
11
000
000
2



Where















323322231213
332313
322212
000
000
1
B
As for stress vector, according to the constitutive law
of elasticity,
es D











12
22
11



For example, in case of plane strain






















)1(2
21
00
01
1
0
1
1
)21)(1(
)1(
v-
v
v-
v
v-
v
vv
vE
D
Then, according to the principle of virtual work,

eee
e
S
T
T
e
K
dS DB B
uf
ue








This is called the stiffness equation of element.
Superposing every stiffness equations of element, we
obtain the stiffness equation of whole domain. F = K u
  dS dST
SS
b
e
T
eseffu  








If body force (fb) is considered, the principle of vir-
tual work need be modified as
2. Fault Analysis
As shown in Figure A2, the Mohr-Coulomb criterion is
written as a linear relationship between shear and normal
stresses,
)( 21
*




v (2)
When we consider the analysis in plane strain condi-
tion, it is possible to calculate the value of third principal
stress (*  ), where

is the Poisson ratio (Timoshenko
and Goodier, 1970). After comparing the values of1

,
2

and *  , we can recognize the newly defined 1

,
2

and 3

as the maximum, intermediate and mini
mum principal stresses respectively. We introduce how
Figure A2. Failure envelope and Mohr’s circle in σ-τ space. c
is cohesion and φ is angle of internal friction (Hayashi, 2008).
mum principal stresses respectively. We introduce how
the Mohr-Coulomb criterion is combined into the FE
software package; though I already wrote the method of
failure analysis in my serial papers (Table 1).
If body force (b f) is considered, the principle of vir-
tual work need be modified as



tan


c (3)
where c and

are the cohesive strength and the an-
gle of internal friction, respectively. Failure will observe
when the Mohr’s circle first touches the failure envelope
(3). It will happen when the radius of the Mohr’s circle,
1

+2

/2, is equal to the perpendicular distance from
the center of the circle at 1

-2

/2 to the failure enve-
lope,




sin
2
cos
2
3131 











c
failure
(4)
According to Melosh and Williams (1989), the prox-
imity to failure (f P) is the ratio between the calculated
stress and the failure stress, which is given by



























failure
f
P
2
2
31
31


(5)
When the ratio reaches one (f P = 1), failure occurs,
but when f
P < 1 stress is within the failure envelope,
rock does not fail. The proximity to failure f P reveals
which parts of the model are close to failure or already
failed by generating faults.
The type of faulting has been determined by the And-
erson’s theory (1951). According to his theory three
classes of faults (normal, strike slip and thrust) result
from the three principal classes of inequality that may
exist between the principal stresses. I realized the judg-
ment in the program failure.state.func in FE package.